Seminar presentation “Nash equilibrium structure of a class of spatial competition games”

Speaker : François Baccelli
Date: 16/09/2020
Time: 2:00 pm - 3:00 pm


We study an N-player game where a pure action of each player is to
select a non-negative function on a Polish space supporting a finite
diffuse measure, subject to a finite constraint on the integral of the
function. This function is used to define the intensity of a Poisson
point process on the Polish space. The processes are independent over
the players, and the value to a player is the measure of the union of
its open Voronoi cells in the superposition point process. Under
randomized strategies, the process of points of a player is thus a Cox
process, and the nature of competition between the players is akin to
that in Hotelling competition games. We characterize when such a game
admits Nash equilibria and prove that when a Nash equilibrium exists, it
is unique and comprised of pure strategies that are proportional in the
same proportions as the total intensities. We give examples of such
games where Nash equilibria do not exist.

This is a joint work with Venkat Anantharam, UC Berkeley, EECS.